The　time-lag　period　is　usually　assumed　to　be　a　fixed　value　in　most　multivariate　grey　prediction　models.　This　assumption　makes　it　hard　to　describe　the　real　characteristics　of　the　analyzed　system.　This　paper　proposes　a　new　modeling　method　based　on　a　generalized　time-delay　function,　which　considers　both　the　dynamics　and　differences　of　time　series.　Then　a　new　model　DGM(1,N,tau(i))　is　designed　and　compared　with　existing　grey　prediction　models.　The　main　advantage　of　the　model　DGM　(1,N　,tau(i))　is　that　it　describes　the　additive　effect　of　time-delay　variables　and　offers　a　new　dynamic　adjustment　method　to　predict　this　effect.　Another　advantage　is　the　generality　of　model　DGM(1,N,tau(i)):　it　can　be　extended　to　several　other　widely　used　grey　models,　such　as　DGM(1,N),　DDGM　(1,N)　and　DDGMD(1,N).　Some　improvements　of　the　classic　grey　incidence　degree　calculation　and　a　new　reverse　flip　sequence　operator　are　provided　to　reduce　the　negative　effect　of　subjective　modeling　factor　selection.　These　optimization　methods　improve　the　stability　of　predictions.　A　case　study　of　China　＇s　agricultural　output　forecast　is　provided　to　test　the　new　model.　It　considers　several　available　sample　scenarios　and　includes　all　situations　that　result　from　the　subjective　judgment　of　modeling　factors.　Results　show　that　the　new　model　can　model　the　complex　effect　of　time　delays,　and　it　also　has　higher　prediction　accuracy　than　the　other　three　classic　models.